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ec_curvedata • Show schema
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{'Ciso': '55a', 'Clabel': '55a1', 'Cnumber': 1, 'abc_quality': 1.0555982735754514, 'absD': 3025, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 220, 'ainvs': [1, -1, 0, -4, 3], 'analytic_rank': 0, 'bad_primes': [5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 55, 'degree': 2, 'elladic_images': ['4.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.63223907025473155537160347037', 'prec': 107}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [8120601, 3025], 'lmfdb_iso': '55.a', 'lmfdb_label': '55.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -4, 3], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0-2.a.1.1', '20.24.0-20.b.1.2', '44.24.0-44.a.1.1', '220.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63223907025473155537160347037', 'prec': 107}, 'szpiro_ratio': 3.9702001278075087, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, -1, 1, 0, 0, -3, -3, 1, -1, 0, 2, 0, 0, -1, 6, -3, -4, -1], 'aplist': [1, 0, 1, 0, -1, 2, 6, -4, 4, 6, -8, -2, 2, 4, -12, -2, 4, -10, -16, 8, 14, 8, -4, 10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 55, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '55.a', 'trace_hash': 467045135390574132}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '3.5412442219130809586031872287', 'prec': 100}, 'conductor': 55, 'gens': [], 'heights': [], 'lmfdb_label': '55.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '4.1146794247127563394669761001', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.0286698561781890848667440250290006511', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[-2, 1, 1], [2, -1, 1]], 'xcoord_integral_points': [-2, 2]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 0], '5': [1, 0], '11': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '55.a3'}
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ec_torsion_growth • Show schema
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id: 1896
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 4]}
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id: 1897
{'degree': 4, 'field': [9, 0, -5, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 4]}
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id: 1898
{'degree': 4, 'field': [16, 0, -3, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 4]}
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id: 1901
{'degree': 8, 'field': [-3, 0, 3, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 6]}
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id: 1900
{'degree': 8, 'field': [1, 0, -4, 0, 1, 0, -4, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 8]}
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id: 1899
{'degree': 8, 'field': [20, -100, 186, -190, 141, -58, 24, -4, 1], 'lmfdb_label': '55.a3', 'torsion': [4, 4]}
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id: 1904
{'degree': 16, 'field': [9, 0, -27, 0, 135, 0, -54, 0, -105, 0, 54, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 12]}
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id: 1902
{'degree': 16, 'field': [121, 0, 484, 0, 374, 0, 308, 0, 355, 0, 212, 0, 74, 0, 16, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 8]}
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id: 1903
{'degree': 16, 'field': [38416, 0, -74480, 0, 67601, 0, 11060, 0, -7309, 0, -200, 0, 371, 0, 20, 0, 1], 'lmfdb_label': '55.a3', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 268
{'conductor': 55, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '55.a3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 269
{'conductor': 55, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '55.a3', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1666015
{'adelic_gens': [[101, 2, 0, 1], [217, 4, 216, 5], [91, 2, 86, 219], [113, 4, 8, 11], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '220.48.0.?', 'conductor': 55, 'lmfdb_label': '55.a3', 'prime': 0}
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id: 168
{'conductor': 55, 'elladic_image': '4.12.0.1', 'lmfdb_label': '55.a3', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 55.a does not appear in ec_padic
